| DataSet | GRT low | GRT high | Distance Threshold | Proximity Criterion | Deers | Observations |
|---|---|---|---|---|---|---|
| 1 | 0 | 36 | 10 | closest in time | 35 | 149 |
| 2 | 0 | 36 | 10 | nearest | 35 | 147 |
| 3 | 0 | 200 | 15 | score | 36 | 223 |
P15.2 Fortgeschrittenes Praxisprojekt
Dr. Nicolas Ferry - Bavarian National Forest Park / Daniel Schlichting - StabLab
31 Jan 2025
Model FCM levels - amongst other covariables - on spatial and temporal distance to hunting activities
Expectations:
Contains information of 809 faecal samples, including:
Samples where taken at irregular time intervals from 2020 to 2022.
Contains location and time of \(\geq\) 700 hunting events from 2020 to 2022.
Other sources of uncertainty include:
unknown characteristics of the deer (e.g., age, health, etc.),
other unknown stressors (e.g., predators, human activities, weather, etc.),
unknown geographical features (e.g., terrain could affect the propagation of sound).
Deer location at the time of hunting event is approximated by linear interpolation:
A hunting event is considered relevant to an FCM sample, if
In the following, GRT thresholds = (0, 50), distance threshold = 10 or 15.
Among the relevant hunting events, the most relevant one is defined by one of the three introduced proximity criteria:
A hunting event is considered relevant to a FCM sample, if
we define the Scoring function as following:
\[ S(d, t) \propto \begin{cases} \frac{1}{d^2} \cdot f_\textbf{t}(t), t \sim \mathcal{N}(\mu, \sigma^2) &|t \leq \mu \\ \frac{1}{d^2} \cdot f_\textbf{t}(t), t \sim \mathcal{Laplace}(\mu, b) &|t > \mu \end{cases} \] where:
\[ \begin{align*} d & \text{: Distance } \\ t & \text{: Time Difference } \\ \mu & \text{: GRT target = 19 hours } \end{align*} \]
The marginal effects of distance and elapsed time since challenge on the score:
We suggest three different Datasets for Modelling
| DataSet | GRT low | GRT high | Distance Threshold | Proximity Criterion | Deers | Observations |
|---|---|---|---|---|---|---|
| 1 | 0 | 36 | 10 | closest in time | 35 | 149 |
| 2 | 0 | 36 | 10 | nearest | 35 | 147 |
| 3 | 0 | 200 | 15 | score | 36 | 223 |
For Modelling, we consider the following covariates, defined for each pair of FCM sample and most relevant hunting event:
We chose two different approaches to Modelling:
Family: Gamma
Log link for interpretability
Let \(i = 1,\dots,N\) be the indices of deer and \(j = 1,\dots,n_i\) be the indices of FCM measurements for each deer
\[ \begin{eqnarray} \textup{FCM}_{ij} &\sim& \mathcal{Ga}\left( \nu, \frac{\nu}{\mu_{ij}} \right) \\ \mu_{ij} &=& \mathbb{E}(\textup{FCM}_{ij}) = \exp(\eta_{ij}) \\ \eta_{ij} &=& \beta_0 + \beta_1 \textup{Pregnant}_{ij} + \beta_2 \textup{NumberOtherHunts}_{ij} + \\ && f_1(\textup{TimeDiff}_{ij}) + f_2(\textup{Distance}_{ij}) + \\ && f_3(\textup{SampleDelay}_{ij}) + f_4(\textup{DefecationDay}_{ij}) + \\ && \gamma_{i}, \\ \gamma_i &\overset{\mathrm{iid}}{\sim}& \mathcal{N}(0, \sigma_\gamma^2). \end{eqnarray} \]



Linear Effects:
| Dataset | Term | Estimate | Std. Error |
|---|---|---|---|
| Closest in Time | (Intercept) | 5.8243844 | 0.0533979 |
| Closest in Time | NumOtherHunts | -0.1370438 | 0.0614158 |
| Nearest | (Intercept) | 5.8123504 | 0.0541316 |
| Nearest | NumOtherHunts | -0.1026115 | 0.0596574 |
| Highest Score | (Intercept) | 5.8882327 | 0.0812529 |
| Highest Score | NumOtherHunts | -0.0112701 | 0.0141569 |
How to minimize spatial and temporal distance at the same time?
How to use a bigger Part of the Data?
Effect of Hunting on Red Deer